When we use the plasmid with insert, uncut plasmid, double digested plasmid, and ladder for gel pic, why there is a need to use single digested plasmid in making a good gel image.
You can also obtain clear pictures after electrophoresis of non-restricted plasmid DNA. There is, however, a whole bunch of different DNA-forms that you see on these gels. There are at least the supercoiled form, the nicked or open circle, often some linearised DNA, and in addition many possible multimers or concatemers. This will give you a complicated pattern, although all of these forms are derived from a single plasmid. After restriction with an endonuclease, cutting only once, all of these forms end up in a linear molecules of identical length, leading to a single band on the gel.
DNA mobility during agarose gel electrophoresis is linked to its actual size and degree of compaction. If running circular DNA, different bands will be observed even though the product is pure (supercoiled, linear and circular relaxed forms do exist simultaneously in a plasmid prep). When single digested, only linear form occurs. The purpose of running agarose gel is to evaluate DNA purity, DNA quantity and DNA size. This is also valid for plasmid in which insert has been cloned: the double digest will go further into analysis by determining the sizes of open plasmid and insert.
The result of a single digest with your plasmid should ideally be cut in only one place, yielding a band on the gel closest to the known base pair length of the plasmid. Uncut plasmid with or without insert may be subject to supercoiling and the corresponding band may appear to be a different size than the single-cut, relaxed plasmid. See the link below for more details.